We propose to re-emphasize the low-level texture information in deep networks for semantic segmentation and related knowledge distillation tasks. Low-level texture feature/knowledge is also of vital importance for characterizing the local structural pattern and global statistical property, such as boundary, smoothness, regularity and color contrast, which may not be well addressed by highlevel deep features. In this paper, we are intended to take full advantage of both structural and statistical texture knowledge and propose a novel Structural and Statistical Texture Knowledge Distillation (SSTKD) framework for semantic segmentation. Specifically, Contourlet Decomposition Module (CDM) is introduced to decompose low-level features with iterative Laplacian pyramid and directional filter bank to mine the structural texture knowledge, and Texture Intensity Equalization Module (TIEM) is proposed to extract and enhance statistical texture knowledge with the corresponding Quantization Congruence Loss (QDL). Moreover, we further put forward the Co-occurrence TIEM (C-TIEM) and generic segmentation frameworks, namely STLNet++ and U-SSNet, to enable existing segmentation networks to harvest the structural and statistical texture information more effectively. Extensive experimental results on three segmentation tasks demonstrate the effectiveness of the proposed methods, showing they achieve state-of-the-art performances on seven popular benchmark datasets, respectively.